The office of the Information Commissioner has confirmed it is investigating claims that the Conservative minister Oliver Letwin has been disposing of government documents in bins in a park close to Downing Street.

The revelation that Letwin, David Cameron's chief policy adviser, has been seen throwing away documents in the park on five occasions has sparked concern about potential security risks as well as data protection breaches.

The Labour leader, Ed Miliband, accused the minister of "treating important papers with contempt" and engaging in "very strange behaviour".

Labour MP and shadow minister without portfolio Michael Dugher has written to the cabinet secretary, Gus O'Donnell, to demand an investigation into the classification of any discarded documents and whether strict procedures for the disposal of government documents were breached.

Downing Street said Letwin had promised not to throw official papers into public bins in future. A spokeswoman said the Cabinet Office was looking into whether any sensitive material had been among the papers dumped.

"Our understanding is that there were no classified documents," she said. "Most of the business Mr Letwin does in the park is constituency based. In the light of what has been reported, the Cabinet Office is looking into it."

She said David Cameron had not yet spoken to Letwin about his use of public bins. Asked what the prime minister's view was, she added: "Clearly, it's not a sensible way to dispose of documents. Mr Letwin has agreed he will not dispose of documents in this way again."

The office of the Information Commissioner is examining whether lax disposal of the documents could involve a breach of the Data Protection Act.

A spokeswoman said: "We are aware of the allegations and are making inquiries. Keeping personal data secure is a key principle of the Data Protection Act, and the ICO takes any breach of that principle very seriously."

Speaking in Leeds, Miliband said: "If it's true that there were constituents who'd written to him and he was looking at constituency letters and they just ended up in the bin, I don't think it's the right way to act and the right way to treat people and people's concerns.

"I think he'll have learnt his lesson, and I hope he does learn his lesson. I think most people would think, you're dealing with sensitive correspondence, you should treat it in a sensitive way."

The Daily Mirror reported that Letwin discarded more than 100 papers, including correspondence on terrorism and national security and constituents' private details.

The paper described the Cabinet Office minister's actions as a "security breach", but a spokesman for Letwin insisted the papers were not of a sensitive nature.

The spokesman said: "Oliver Letwin does some of his parliamentary and constituency correspondence in the park before going to work, and sometimes disposes of copies of letters there."

One of the documents thrown away by Letwin was said to describe how intelligence chiefs "failed to get the truth" about Britain's involvement in terrorist interrogations.

In his letter to O'Donnell, Dugher wrote: "Civil servants are subject to disciplinary procedures if the proper processes are not adhered to. It cannot be that there is one rule for ministers and another for everyone else."

Letwin, the MP for West Dorset, is an early riser who does a morning circuit of St James's Park, usually starting at 5.30am. In this period he dictates letters for typing by his secretary during the day.

The Labour backbencher Jeremy Corbyn told Radio 5 Live that while he enjoyed the "idea of ministers walking around the park in the morning", carrying confidential documents was wrong.

"It's a remarkably silly thing to do," the MP for Islington North said. "To then dump them all in a bin is really very stupid, because he could easily be spotted and followed and anybody could then pick them up.

"There are plenty of ways of getting rid of sensitive documents. All the parliamentary papers are shredded and so are the ones in the House of Commons and presumably the ministry as well."

The revelations present a further headache for Cameron in a week during which Downing Street has been forced onto the back foot over the defence secretary, Liam Fox.

Zac Goldsmith, the Tory MP for Richmond, tweeted: "How is Oliver Letwin working in the park newsworthy?! Whoever in Labour has asked for (yet another) inquiry shd be put to sleep."